Constructing elliptic curves with a known number of points over a prime field, High Primes and Misdemeanours: Lectures in Honour of the 60th Birthday of, Fields Institute Communications, 2004. ,
Prime sieves using binary quadratic forms, Mathematics of Computation, vol.73, issue.246, pp.1023-1030, 2004. ,
DOI : 10.1090/S0025-5718-03-01501-1
Elliptic curves and primality proving, Mathematics of Computation, vol.61, issue.203, pp.29-68, 1993. ,
DOI : 10.1090/S0025-5718-1993-1199989-X
URL : https://hal.archives-ouvertes.fr/inria-00075302
Explicit bounds for primality testing and related problems, Mathematics of Computation, vol.55, issue.191, pp.355-380, 1990. ,
DOI : 10.1090/S0025-5718-1990-1023756-8
Constructing elliptic curves with prescribed embedding degrees, Security in Communication Networks ? Third International Conference, pp.257-267, 2002. ,
Fast Multiple-Precision Evaluation of Elementary Functions, Journal of the ACM, vol.23, issue.2, pp.242-251, 1976. ,
DOI : 10.1145/321941.321944
Elliptic curves suitable for pairing based cryptography, Designs, Codes and Cryptography, pp.133-141, 2005. ,
Effective lower and upper bounds for the Fourier coefficients of powers of the modular invariant j, Journal of the Ramanujan Mathematical Society, vol.20, pp.255-282, 2005. ,
Constructing elliptic curves of prescribed order, Proefschrift, 2006. ,
Elliptic Curves with a Given Number of Points, Lecture Notes in Computer Science, vol.3076, pp.117-131, 2004. ,
DOI : 10.1007/978-3-540-24847-7_8
Un metodo per la risoluzione della congruenza di secondo grado, pp.153-163, 1903. ,
A course in computational algebraic number theory, Graduate Texts in Mathematics, vol.138, 1993. ,
DOI : 10.1007/978-3-662-02945-9
Action of Modular Correspondences around CM Points, Lecture Notes in Computer Science, vol.2369, pp.234-243, 2002. ,
DOI : 10.1007/3-540-45455-1_19
Primes of the form x 2 + ny 2 ? Fermat, class field theory, and complex multiplication, 1989. ,
Erläuterungen zu den vorstehenden Fragmenten, Bernhard Riemann's gesammelte mathematische Werke und wissenschaftlicher Nachlaß, pp.1876-438 ,
Die Typen der Multiplikatorenringe elliptischer Funktionenk??rper, Die Klassenkörper der komplexen Multiplikation, pp.197-272, 1941. ,
DOI : 10.1007/BF02940746
Fast evaluation of modular functions using Newton iterations and the AGM, To appear in Mathematics of Computation, 2007. ,
Building Curves with Arbitrary Small MOV Degree over Finite Prime Fields, Journal of Cryptology, vol.18, issue.2, pp.79-89, 2005. ,
DOI : 10.1007/s00145-004-0219-7
URL : https://hal.archives-ouvertes.fr/inria-00386299
mpfrcx ? a library for univariate polynomials over arbitrary precision real or complex numbers, Version 0 ,
Comparing Invariants for Class Fields of Imaginary Quadratic Fields, Lecture Notes in Computer Science Further investigations of the generalised Weber functions, pp.252-266, 2002. ,
DOI : 10.1007/3-540-45455-1_21
Constructing elliptic curves over finite fields using double eta-quotients, Journal de Th??orie des Nombres de Bordeaux, vol.16, issue.3, pp.555-568, 2004. ,
DOI : 10.5802/jtnb.460
URL : http://archive.numdam.org/article/JTNB_2004__16_3_555_0.pdf
mpc ? a library for multiprecision complex arithmetic with exact rounding, Version 0.4 ,
Evolutio producti infiniti (1?x)(1?xx)(1?x 3 )(1?x 4 )(1?x 5 )(1?x 6 ) etc. in seriem simplicem, Acta academiae scientiarum Petropolitanae 1780:I (1783), Opera Omnia I, vol.3, pp.125-169472 ,
Faster integer multiplication, Proceedings of the 39th Annual ACM Symposium on Theory of Computing ? STOC'07, pp.57-66, 2007. ,
Modern computer algebra, 1999. ,
Computing Frobenius maps and factoring polynomials, Computational Complexity, vol.2, pp.187-224, 1992. ,
Class invariants by Shimura's reciprocity law, Journal de Th??orie des Nombres de Bordeaux, vol.11, issue.1, pp.45-72, 1999. ,
DOI : 10.5802/jtnb.238
Generating class fields using Shimura reciprocity, Lecture Notes in Computer Science, vol.1423, pp.441-453, 1998. ,
DOI : 10.1007/BFb0054883
gmp ? GNU multiprecision library ,
mpfr ? a library for multiple-precision floating-point computations with exact rounding ,
Algorithms in Number Theory, Handbook of Theoretical Computer Science, pp.673-715, 1990. ,
DOI : 10.1016/B978-0-444-88071-0.50017-5
Elliptic curves with complex multiplication, Communication sur la Number Theory List, 2004. ,
New explicit conditions of elliptic curve traces for FR-reduction, IEICE Trans. Fundamentals E84-A, issue.5, pp.1234-1243, 2001. ,
Die singulären Werte der Weberschen Funktionen f, f 1 Journal für die reine und angewandte 38. , Weber's class invariants revisited, Mathematik Journal de Théorie des Nombres de Bordeaux, vol.3287, issue.14 1, pp.46-74, 1976. ,
Fast multiplication of large numbers, Computing, vol.150, issue.3-4, pp.281-292, 1971. ,
DOI : 10.1007/BF02242355
Fast reduction and composition of binary quadratic forms, Proceedings of the 1991 international symposium on Symbolic and algebraic computation , ISSAC '91, pp.128-133, 1991. ,
DOI : 10.1145/120694.120711
The exponents of the groups of points on the reductions of an elliptic curve, Arithmetic Algebraic Geometry, Birkhäuser, pp.325-335, 1991. ,